Lower Elementary:
Question: Jane is buying 8 pencils. What is the total if each pencil costs 40 cents?
Answer: $3.20
Solution: Count by 40, 8 times. 40, 80, 120, 160, 200, 240, 280, 320. Alternatively, counting something 8 times is the same as doubling 3 times (2×2×2 = 8). 40 doubled is 80, 80 doubled is 160, 160 doubled is 320. The total comes to 320 cents, or $3.20.
Upper Elementary:
Question: Mimi is making a muffin mix. The recipe for the mix calls for 1 1/2 cups of flour, 1/3 cup of sugar, and 1/6 cup of brown sugar. What is the total amount in cups of the mix?
Answer: 2 cups
Solution: In order to add the fractions, we use the Law of Sameness so that all the fractions have the same name. In this problem, the fractions should all be sixths (since that is the smallest number that 2, 3, and 6 all go into [or LCM]).
1.5 can be written as 1 1/2. 1 1/2 = 1 3/6.
1/3 = 2/6.
Now our 3 fractions are 1 3/6, 2/6, and 1/6. Adding them together, we get 1 6/6 cups, which is the same as 2 cups.
Middle School:
Question: 3 marbles cost $4.50. How much would 8 marbles cost?
Answer: $12
Solution: We can solve this by finding the unit price of the marbles. We know 3 marbles cost $4.50. To find the unit price, divide by 3. 1 marble costs $1.50. Now multiply the cost of 1 marble by 8 to get the total cost. Multiplying by 8 is the same as doubling 3 times: $1.50 doubled is $3, $3 doubled is $6, $6 doubled is $12. 8 marbles cost $12.
Algebra and Up:
Question: A moving truck rental service charges an initial cost of $250. The first 50 miles are free and after that its $20 per mile. If Mark paid $470, how many miles did he drive?
Answer: 61 miles
Solution: Let m be the number of miles Mark drives beyond 50 miles and let T be the total. If we write this problem as an equation, it would be T = 20m + 250. We know the total is $470, so we will substitute 470 for T so we can solve for m.
470 = 20m + 250
220 = 20m
11 = m
So Mark drove another 11 miles in addition to the 50 miles that were free. Mark drove a total of 61 miles.
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